{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:49:49Z","timestamp":1760150989308,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,10]],"date-time":"2022-02-10T00:00:00Z","timestamp":1644451200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Spatially-varying intensity noise is a common source of distortion in medical images and is often associated with reduced accuracy in medical image registration. In this paper, we propose two multi-resolution image registration algorithms based on Empirical Mode Decomposition (EMD) that are robust against additive spatially-varying noise. EMD is a multi-resolution tool that decomposes a signal into several principle patterns and residual components. Our first proposed algorithm (LR-EMD) is based on the registration of EMD feature maps from both floating and reference images in various resolutions. In the second algorithm (AFR-EMD), we first extract a single average feature map based on EMD and then use a simple hierarchical multi-resolution algorithm to register the average feature maps. We then showcase the superior performance of both algorithms in the registration of brain MRIs as well as retina images. For the registration of brain MR images, using mutual information as the similarity measure, both AFR-EMD and LR-EMD achieve a lower error rate in intensity (42% and 32%, respectively) and lower error rate in transformation (52% and 41%, respectively) compared to intensity-based hierarchical registration. Our results suggest that the two proposed algorithms offer robust registration solutions in the presence of spatially-varying noise.<\/jats:p>","DOI":"10.3390\/a15020058","type":"journal-article","created":{"date-parts":[[2022,2,11]],"date-time":"2022-02-11T02:37:46Z","timestamp":1644547066000},"page":"58","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Robust Registration of Medical Images in the Presence of Spatially-Varying Noise"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7824-4628","authenticated-orcid":false,"given":"Reza","family":"Abbasi-Asl","sequence":"first","affiliation":[{"name":"Department of Neurology, Department of Bioengineering and Therapeutic Sciences, University of California, San Francisco, CA 94143, USA"},{"name":"Weill Institute for Neurosciences, University of California, San Francisco, CA 94143, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8813-3462","authenticated-orcid":false,"given":"Aboozar","family":"Ghaffari","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Iran Science and Technology University, Tehran 16844, Iran"}]},{"given":"Emad","family":"Fatemizadeh","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Sharif University of Technology, Tehran 14115, Iran"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.1109\/TMI.2013.2265603","article-title":"Deformable medical image registration: A survey","volume":"32","author":"Sotiras","year":"2013","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"34461","DOI":"10.1038\/srep34461","article-title":"Liver DCE-MRI registration in manifold space based on robust principal component analysis","volume":"6","author":"Feng","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_3","unstructured":"Brooks, R.R., and Iyengar, S.S. (1998). Multi-Sensor Fusion: Fundamentals and Applications with Software, Prentice-Hall, Inc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"15051","DOI":"10.1038\/srep15051","article-title":"Fully automatic and robust 3D registration of serial-section microscopic images","volume":"5","author":"Wang","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6050","DOI":"10.1038\/srep06050","article-title":"Robust image registration of biological microscopic images","volume":"4","author":"Wang","year":"2014","journal-title":"Sci. Rep."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"7583","DOI":"10.1038\/s41598-018-25922-7","article-title":"Accurate and fiducial-marker-free correction for three-dimensional chromatic shift in biological fluorescence microscopy","volume":"8","author":"Matsuda","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_7","unstructured":"Lucas, B.D., and Kanade, T. (1981, January 24\u201328). An iterative image registration technique with an application to stereo vision. Proceedings of the Image Understanding Workshop, Vancouver, BC, Canada."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1038\/s41598-017-00492-2","article-title":"Augmented reality with image registration, vision correction and sunlight readability via liquid crystal devices","volume":"7","author":"Wang","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1016\/j.ijrobp.2005.10.027","article-title":"Feasibility of a novel deformable image registration technique to facilitate classification, targeting, and monitoring of tumor and normal tissue","volume":"64","author":"Brock","year":"2006","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1038\/35004593","article-title":"Growth patterns in the developing brain detected by using continuum mechanical tensor maps","volume":"404","author":"Thompson","year":"2000","journal-title":"Nature"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S1361-8415(02)00063-4","article-title":"Image registration via level-set motion: Applications to atlas-based segmentation","volume":"7","author":"Vemuri","year":"2003","journal-title":"Med. Image Anal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1080\/10255842.2012.670855","article-title":"Medical image registration: A review","volume":"17","author":"Oliveira","year":"2014","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1109\/TMI.2002.1009381","article-title":"Consistent landmark and intensity-based image registration","volume":"21","author":"Johnson","year":"2002","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Ghanbari, A., Abbasi-Asl, R., Ghaffari, A., and Fatemizadeh, E. (2012, January 17\u201319). Automatic b-spline image registration using histogram-based landmark extraction. Proceedings of the 2012 IEEE-EMBS Conference on Biomedical Engineering and Sciences, Langkawi, Malaysia.","DOI":"10.1109\/IECBES.2012.6498119"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1421","DOI":"10.1109\/TMI.2002.803111","article-title":"HAMMER: Hierarchical attribute matching mechanism for elastic registration","volume":"21","author":"Shen","year":"2002","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1109\/TMI.2009.2028078","article-title":"Feature based nonrigid brain MR image registration with symmetric alpha stable filters","volume":"29","author":"Liao","year":"2010","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Abbasi-Asl, R., and Fatemizadeh, E. (2011, January 16\u201317). MMRO: A feature selection criterion for mr images based on alpha stable filter responses. Proceedings of the 7th Iranian Conference on Machine Vision and Image Processing (MVIP), Tehran, Iran.","DOI":"10.1109\/IranianMVIP.2011.6121607"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/S1361-8415(01)80004-9","article-title":"Multi-modal volume registration by maximization of mutual information","volume":"1","author":"Wells","year":"1996","journal-title":"Med. Image Anal."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1109\/42.563664","article-title":"Multimodality image registration by maximization of mutual information","volume":"16","author":"Maes","year":"1997","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"13112","DOI":"10.1038\/s41598-018-31474-7","article-title":"Groupwise image registration based on a total correlation dissimilarity measure for quantitative MRI and dynamic imaging data","volume":"8","author":"Guyader","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1109\/TMI.2006.872745","article-title":"Deformation-based mapping of volume change from serial brain MRI in the presence of local tissue contrast change","volume":"25","author":"Studholme","year":"2006","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1882","DOI":"10.1109\/TMI.2010.2053043","article-title":"Intensity-based image registration by minimizing residual complexity","volume":"29","author":"Myronenko","year":"2010","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5567","DOI":"10.1109\/TIP.2015.2479462","article-title":"RISM: Single-modal image registration via rank-induced similarity measure","volume":"24","author":"Ghaffari","year":"2015","journal-title":"IEEE Trans. Image Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1109\/TMI.2017.2744663","article-title":"Image Registration based on Low Rank Matrix: Rank-Regularized SSD","volume":"37","author":"Ghaffari","year":"2018","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.compbiomed.2016.03.022","article-title":"Medical image registration using sparse coding of image patches","volume":"73","author":"Afzali","year":"2016","journal-title":"Comput. Biol. Med."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.sigpro.2014.10.022","article-title":"Robust Huber similarity measure for image registration in the presence of spatially-varying intensity distortion","volume":"109","author":"Ghaffari","year":"2015","journal-title":"Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Pohl, K.M., Fisher, J., Levitt, J.J., Shenton, M.E., Kikinis, R., Grimson, W.E.L., and Wells, W.M. (2005, January 26\u201329). A unifying approach to registration, segmentation, and intensity correction. Proceedings of the Medical Image Computing and Computer-Assisted Intervention\u2014MICCAI 2005, Palm Springs, CA, USA.","DOI":"10.1007\/11566465_39"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1002\/hbm.460030303","article-title":"Spatial registration and normalization of images","volume":"3","author":"Friston","year":"1995","journal-title":"Hum. Brain Mapp."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. Lond. Math. Phys. Eng. Sci. R. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1049\/iet-ipr.2012.0034","article-title":"Medical image registration based on fast and adaptive bidimensional empirical mode decomposition","volume":"7","author":"Riffi","year":"2013","journal-title":"IET Image Process."},{"key":"ref_31","first-page":"12","article-title":"Multimodal image registration based on empirical mode decomposition and mutual information","volume":"10","author":"Jinsha","year":"2009","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.image.2017.04.003","article-title":"Fast medical image registration using bidirectional empirical mode decomposition","volume":"59","author":"Guryanov","year":"2017","journal-title":"Signal Process. Image Commun."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1626","DOI":"10.1109\/TSP.2008.2011836","article-title":"Multiscale image fusion using complex extensions of EMD","volume":"57","author":"Looney","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"692","DOI":"10.1109\/PROC.1973.9150","article-title":"A digital signal processing approach to interpolation","volume":"61","author":"Schafer","year":"1973","journal-title":"Proc. IEEE"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1109\/83.136597","article-title":"Image coding using wavelet transform","volume":"1","author":"Antonini","year":"1992","journal-title":"IEEE Trans. Image Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1597","DOI":"10.1098\/rspa.2003.1221","article-title":"A study of the characteristics of white noise using the empirical mode decomposition method","volume":"460","author":"Wu","year":"2004","journal-title":"Proc. R. Soc. Lond. Math. Phys. Eng. Sci. R. Soc."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1002\/asmb.501","article-title":"Applications of Hilbert\u2013Huang transform to non-stationary financial time series analysis","volume":"19","author":"Huang","year":"2003","journal-title":"Appl. Stoch. Model. Bus. Ind."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1109\/TSTE.2014.2365580","article-title":"A comparative study of empirical mode decomposition-based short-term wind speed forecasting methods","volume":"6","author":"Ren","year":"2015","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/TNSRE.2012.2229296","article-title":"Classification of motor imagery BCI using multivariate empirical mode decomposition","volume":"21","author":"Park","year":"2013","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.sigpro.2017.01.022","article-title":"A joint framework for multivariate signal denoising using multivariate empirical mode decomposition","volume":"135","author":"Hao","year":"2017","journal-title":"Signal Process."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1016\/S0262-8856(03)00094-5","article-title":"Image analysis by bidimensional empirical mode decomposition","volume":"21","author":"Nunes","year":"2003","journal-title":"Image Vis. Comput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/BF02857540","article-title":"A technique to improve the empirical mode decomposition in the Hilbert-Huang transform","volume":"2","author":"Chen","year":"2003","journal-title":"Earthq. Eng. Eng. Vib."},{"key":"ref_43","unstructured":"(2013, January 10). Available online: http:\/\/www.bic.mni.mcgill.ca\/brainweb\/."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1109\/42.796284","article-title":"Nonrigid registration using free-form deformations: Application to breast MR images","volume":"18","author":"Rueckert","year":"1999","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_45","unstructured":"Cocosco, C.A., Kollokian, V., Kwan, R.K.S., Pike, G.B., and Evans, A.C. (2013, January 10). Brainweb: Online Interface to a 3D MRI Simulated Brain Database. NeuroImage. Citeseer. Available online: http:\/\/www.bic.mni.mcgill.ca\/users\/crisco\/HBM97_poster\/HBM97_poster.pdf."},{"key":"ref_46","unstructured":"(2013, January 10). Available online: http:\/\/www.cma.mgh.harvard.edu\/ibsr\/."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"16","DOI":"10.35119\/maio.v1i4.42","article-title":"FIRE: Fundus image registration dataset","volume":"1","author":"Zabulis","year":"2017","journal-title":"Model. Artif. Intell. Ophthalmol."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1186\/1687-5281-2013-25","article-title":"An efficient approach for robust multimodal retinal image registration based on UR-SIFT features and PIIFD descriptors","volume":"2013","author":"Ghassabi","year":"2013","journal-title":"EURASIP J. Image Video Process."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.1109\/TMI.2003.819276","article-title":"The dual-bootstrap iterative closest point algorithm with application to retinal image registration","volume":"22","author":"Stewart","year":"2003","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_50","first-page":"423","article-title":"A region merging algorithm using mathematical morphology: Application to macula detection","volume":"12","author":"Zana","year":"1998","journal-title":"Comput. Imaging Vis."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1109\/72.97934","article-title":"A general regression neural network","volume":"2","author":"Specht","year":"1991","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"704182","DOI":"10.3389\/fdata.2021.704182","article-title":"Structural Compression of Convolutional Neural Networks with Applications in Interpretability","volume":"4","author":"Yu","year":"2021","journal-title":"Front. Big Data"},{"key":"ref_54","unstructured":"Abbasi-Asl, R., and Yu, B. (2017). Interpreting Convolutional Neural Networks Through Compression. arXiv."},{"key":"ref_55","unstructured":"Vellido, A., Mart\u00edn-Guerrero, J.D., and Lisboa, P.J. (2012, January 25\u201327). Making machine learning models interpretable. Proceedings of the ESANN 2012 proceedings: European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, Bruges, Belgium."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"22071","DOI":"10.1073\/pnas.1900654116","article-title":"Definitions, methods, and applications in interpretable machine learning","volume":"116","author":"Murdoch","year":"2019","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/978-3-642-21729-6_42","article-title":"Estimation of muscle force with emg signals using hammerstein-wiener model","volume":"35","author":"Khorsandi","year":"2011","journal-title":"IFMBE Proc. BIOMED"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/BF00341929","article-title":"The identification of nonlinear biological systems: Wiener and Hammerstein cascade models","volume":"55","author":"Hunter","year":"1986","journal-title":"Biol. Cybern."},{"key":"ref_59","first-page":"45","article-title":"Hammerstein-Wiener Model: A New Approach to the Estimation of Formal Neural Information","volume":"3","author":"Khorsandi","year":"2012","journal-title":"Basic Clin. Neurosci."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/2\/58\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:17:30Z","timestamp":1760134650000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/2\/58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,10]]},"references-count":59,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["a15020058"],"URL":"https:\/\/doi.org\/10.3390\/a15020058","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2022,2,10]]}}}